## The Most Valuable Everyday Math Skill

- by Brett Berry - Wed, 06/01/2016 - 06:13

* Percentages*.

*They come up all the time, in the most casual places. While shopping, dining out, grabbing a latte, checking grades, banking, taxes, … need I go on?*

That makes them the **most valuable everyday math skill **I can teach *you.*

I’m proud to say my mom taught me this trick when I was very young. We’d spend Saturdays shopping clearance racks and she’d quiz me over and over again, having me calculate the discounts in my head. Needless to say, I got pretty darn good with percents!

**I cannot stress enough how much I want you to master this!**

The next time you’re out dining, I want you to fill in the tip on your receipt with *confidence* and *gusto* and without even one glance at your phone calculator.

## A Little Trick

A percent represents how many of something there are per 100, e.g. 15% means fifteen per one-hundred.

Of course most of the time we are not taking a percentage of 100, but of a different value.

For example, let’s begin by finding 10% of 250.

## The 10% Trick

*To calculate 10% of a number, move the decimal point one position left.*

Here are some examples to illustrate:

_{Note the decimal point is always immediately after the one’s place, even if not shown.}

*Why does this work?* Let’s take a closer look.

Suppose we were calculating 10% of 250 long-hand. I would begin by rewriting 10% as 10/100 and swap out the keyword of for a multiplication symbol.

Then reduce 10/100 by canceling the factors of 10.

When learned that when dividing by 10, we move the decimal point one place to the left. Therefore,

## Calculating Restaurant Tips

Using our trick, we can calculate common tip percentages of 10%, 15% and 20% mentally.

Suppose your dinner bill comes to $48.50.

### 10% Tip Mentally

To find 10%, **use the 10% trick **and move the decimal point one place left.

### 15% Tip Mentally

To calculate 15%, we **combine 10% and 5%** of $48.50.

5 percent is half of 10 percent. So 5 percent of $48.50 will be half of 10 percent of $48.50.

##### Note I rounded $2.425 to the nearest penny, $2.43

For practical purposes you can approximate the tip, so feel free to round this up to $2.50.

Finally combine the 10 percent with the 5 percent value. Using rounded values to approximate 15% we obtain:

Which is only 22 cents away from the exact value of 15% of $48.50.

## 20% Tip Mentally

Suppose we’d like to tip 20%. To do this we’ll **double our 10 percent value** because 2 x 10 percent = 20 percent.

Again we may wish to approximate instead.

Therefore, approximately 20% of $48.50 is $10.

## Calculating Discounts

Another everyday scenario where you might encounter percents is while shopping.

For example, suppose we have a sub-total of $168.75. Let’s calculate a variety of possible discounts.

## 10% off

First take 10 percent of $168.75.

##### Note we rounded $16.875 to the nearest penny, which is $16.88

Since it is 10% off, subtract $16.88 from $168.75.

An estimate will suit our purposes so round $168.75 and $16.88 to the nearest dollar and then subtract.

Our estimation is very close, only 13 cents over the exact answer.

## 25% off

Now let’s try 25% off.

We have two options for finding 25% mentally:

- 25% is one-fourth of 100 percent, so we may divide our total by 4.
- we may compose 25% by adding two 10%’s and one 5%.

*Option One:*

For our purposes, an estimate is fine so let’s begin by rounding $168.75 to $170. I’ll then use __strategic division__ to divide $170 mentally.

*Note*: If you struggle to perform those divisions mentally, you may wish to split them into pieces and divide individually. For example, 170 = 160 + 10.

*Which yields*

*Likewise, $85 ÷ 2 can be split apart and divided individually by 2 to yield $42.50.*

So $42.50 is 25% of $170. Hence our total after discount is approximately $127.50.

*Option Two:*

Using this method we’ll compose 25% from 10% and 5%.

First, approximate 10% of $170.

Secondly, find 5% by dividing 10% in half.

Now we’ll combine two 17’s and an 8.5 to obtain an approximation for 25%.

Again, we arrived at a discount of $42.50, which yields a total of $127.50.

## 30% off

To calculate 30%, we need to add together three 10%’s. We’ve already approximated 10% as 17, so simply add three 17’s together.

##### Notice I added 17 in stages to make it easier to sum mentally

Therefore 30% off is $51 off. Meaning that the total after discount is approximately $119.

##### Mentally, I subtract $51 by first subtracting the tens and then the ones

## 50% off

Fifty percent is simply half off. So all we need to do is divide 170 by 2.

Therefore, the total after discount is $85.

That’s a great start! These techniques will aid you in most percentages you’ll experience day-to-day. In the next lesson, we’ll take an in depth look at how to mentally calculate percentages to the exact percent.

Brett Berry is a math evangelist who writes a math blog for Medium.com called Math Memoirs.